Question

State whether the following statement is true or false.

$\log 540=2\log 2+3\log 3+\log 5$.

• A. True
• B. False

Answer 1

The correct option is A True

$\log 540=2\log 2+3\log 3+\log 5$

$\Rightarrow$ $L.H.S=\log \left(540\right)$

$=\log (4\times 27\times 5)$

$=\log (2^2\times 3^3\times 5)$

$=\log 2^2+\log 3^3+\log 5$ [ By law of product ]

$=2\log 2+3\log 3+\log 5$ [ By law of exponent ]

$=R.H.S$

$\therefore$ $\log 540=2\log 2+3\log 3+\log 5$